Evaluation of Quasi-Periodic Oscillations for the Dynamic Design of Dual Spool Jet Engines Utilizing a Solution of the Invariant Manifold

Abstract Dual spool jet engine dynamic design is nowadays based on approximations of time periodic solutions which is of low computational cost. This paper utilizes a solution of the invariant manifold for the computation of quasi-periodic oscillations of dual spool jet engines which are sourced to the incommensurable ratio of rotating speeds of the two rotors, driven by flow parameters. An invariant manifold is a geometric structure in a dynamical system with the property that solutions which start on the manifold, and follow the evolution prescribed by the differential equation, remain on the manifold. A whole engine dynamic model is established, and local nonlinearities are included by enhanced models of five ball bearings, and a simplified model of one squeeze film damper, existing in a typical configuration of a civil aircraft engine. The quasi-periodic response limit cycles are evaluated for a virtual run-up of the engine applying numerical continuation. Stability assessment of the quasi-periodic limit cycles is performed by evaluating Lyapunov exponents. Four different versions of the rotor-bearing system are investigated, with respect to the number of nonlinear support elements (ball bearings and squeeze film damper). The results demonstrate the need for incorporating quasi-periodic solutions in the dynamic design of machines of this type, with focus on a) the instability issues which cannot be predicted by periodic solutions, b) to the unbalance response amplitude which appears to differ when comparing periodic and quasi-periodic response, and c) to the additional frequency content in the response of the nonlinear quasi-periodic system.